CAIRO — New cracks emerged in the government of Egyptian President Mohammed Morsi on Sunday over his decree claiming power beyond the review of any court in the country, which has been met with loud protests.

While Morsi defended his decree and insisted that it was temporary, his justice minister, Ahmed Mekki, began arguing publicly for a retreat that might defuse an escalating battle between Egypt’s new Islamist leaders and the institutions of its old secular authoritarian government.

Clashes involving the opposition were reported Sunday in Cairo for a third day and the president’s Muslim Brotherhood has called for rival demonstrations. A teenager was killed and at least 40 people were wounded when a group of anti-Morsi protesters tried to storm the political offices of the Muslim Brotherhood in Damanhoor, the Associated Press reported.

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Mekki, an influential former leader of the movement for judicial independence under Hosni Mubarak, is now one of Morsi’s closest advisers. He said on two television talk shows late Saturday night that he objected to the scope of the president’s decree, which his opponents say could be a first step toward a new Islamist autocracy.

The president’s office has said the decree was needed to protect the democratically chosen constituent assembly that is trying to write a new Egyptian Constitution from Mubarak-appointed judges who appeared poised to dissolve it.

Mekki said he supported that goal but that the president could accomplish it with a much narrower edict, one that did not assert sweeping immunity from judicial review on other matters, the feature of the decree Morsi issued on Thursday that has prompted the loudest protests.

On Sunday, Mekki met with the highest council overseeing the Egyptian courts to discuss the matter, and the council issued a statement of its own that scholars said appeared to endorse Mekki’s proposed compromise. Morsi is scheduled to meet with his advisers to discuss it Tuesday morning.

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‘‘In his head, the president thought that this would push us forward, but then it was met by all this inflammation,’’ Mekki said. He faulted the president for failing to consult with opponents before issuing it; he also faulted the opponents for their unwillingness to come to the table.

On Saturday, judges across Egypt rebelled against the decree. A coalition of opposition leaders, including the former United Nations diplomat Mohamed ElBaradei and three other former Egyptian presidential candidates, demanded that the decree be canceled.

On the first day of trading since the decree was issued, Egypt’s stock market fell about 9.5 percent over concerns that the latest standoff could bring more instability.

Morsi, Egypt’s first freely elected president and a former leader of the Muslim Brotherhood, now faces a test of his ability and willingness to engage in the kind of compromise that democratic government requires. But he also faces real doubts about the willingness of his secular-minded opponents to join him in compromise.

Each side is mired in suspicion of the other, a legacy of the decades when the Brotherhood survived here only as an insular secret society, demonized as dangerous radicals by most of the Egyptian elite.

Some conflicting signals emerged Sunday from people close to the president. The president’s office issued a statement stressing that the decree was meant to last only until the country approves a new constitution and that Morsi was committed to reaching a national consensus on what that new constitution should say.